Travel-sick City crashed to their third away defeat in a week and fifth on the trot.
They remain outside of the play-offs after another result that will leave huge question marks against their potential to finish in the top seven.
As the season reaches critical point, they have suffered their biggest slump.
Bournemouth needed only four minutes to go in front as warhorse striker Steve Fletcher was given time and space to slot home from ten yards.
Barry Conlon, in for the injured Peter Thorne, was denied by a fine save from Shwan Jalal. But City levelled after 24 minutes when Matt Clarke, like Conlon back from his disciplinary absence at the weekend, powered home Nicky Law's free-kick.
Brett Pitman thought he had restored Bournemouth's lead straight from a corner only to see it ruled out for an infringement.
But the Cherries struck twice in a couple of minutes just before half-time to take a firm grip on the game.
Mark Molesley fed Fletcher for his second goal and then Jeff Goulding cashed in on a horrible mix-up between Clarke and Graeme Lee to make it three.
And Goulding killed off any faint hopes of a City recovery six minutes after the break when he slammed home Bournemouth's fourth.
CITY: Evans, Arnison, Lee, Clarke, Rehman, Jones, Furman, Law, Brandon, Boulding, Conlon. Subs: McLaren, Bullock, Colbeck, O'Brien, Gillespie.